Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation

Abstract

An investigation on the effect of uniform tensile in-plane force on the radially symmetric vibratory characteristics of functionally graded circular plates of linearly varying thickness along radial direction and resting on a Winkler foundation has been carried out on the basis of classical plate theory. The non-homogeneous mechanical properties of the plate are assumed to be graded through the thickness and described by a power function of the thickness coordinate. The governing differential equation for such a plate model has been obtained using Hamilton's principle. The differential transform method has been employed to obtain the frequency equations for simply supported and clamped boundary conditions. The effect of various parameters like volume fraction index, taper parameter, foundation parameter and the in-plane force parameter has been analysed on the first three natural frequencies of vibration. By allowing the frequency to approach zero, the critical buckling loads for both the plates have been computed. Threedimensional mode shapes for specified plates have been plotted. Comparison with existing results has been made.

Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

“…Authors of many previous papers (e.g., [26][27][28][29][30]) presented the free transverse vibration analysis of the perfect (without porosity) FGM circular plates using the equation of motion including only the coefficient of the pure bending stiffness varying in the thickness direction of the plate. The coefficients of the extensional stiffness and the bending-extensional coupling stiffness were neglected because the effect of the coupled in-plane and transverse displacements was omitted for obtaining simplified solution to the eigenvalue problem.…”

Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates

“…Authors of many previous papers (e.g. [27], [28], [29], [30]) presented the free vibration analysis of the perfect (without porosity) FGM circular plates using the equation of motion including only the coefficient of the pure bending stiffness varying in the thickness direction of the plate. The coefficients of the extensional stiffness and the bending-extensional coupling stiffness were neglected because the effect of the coupled in-plane and transverse displacements was omitted for obtaining simplified solution to the eigenvalue problem.…”

An Analytical Closed-Form Solution for Free Vibration of Functionally Graded Circular Plates with Even and Uneven Porosity Distributions

“…Authors of many previous papers (e.g. [27], [28], [29], [30]) presented the free vibration analysis of the perfect (without porosity) FGM circular plates using the equation of motion including only the coefficient of pure bending stiffness varying in the thickness direction of the plate, but the coefficients of extensional stiffness and bending-extensional coupling stiffness were neglected because the effect of the coupled in-plane and transverse displacements was omitted. As a result, the authors obtained the approximate model of functionally graded material and considered its effect on the natural frequencies of circular plates with the additional complicating effects.…”

“…By substituting the obtained forms from Eqs. (29) into Eq. 27, the generalized ordinary differential equation with variable coefficients is obtained as:…”